This image reconstruction processing method is used in the whole image reconstruction technique of tomographic imaging apparatus (CT (Computed Tomography) apparatus) with radiation detecting apparatus. The tomographic imaging apparatus with the radiation detecting apparatus include, for example, nuclear medicine diagnostic apparatus and X-ray computerized tomographic apparatus (X-ray CT apparatus). The reconstruction process is performed for reconstructing, from a measurement data set of a subject obtained by the radiation detecting apparatus, a physical quantity distribution of the subject relating to an occurrence factor of the measurement data set as a multidimensional digital image (such as a sectional image or a 3D reconstruction image).
The nuclear medicine diagnostic apparatus include a positron emission tomographic apparatus (PET (Positron Emission Tomography) apparatus) and a single photon emission tomographic apparatus (SPECT (Single Photon Emission CT) apparatus). The PET apparatus detects a plurality of radioactive rays (gamma rays) generated by annihilation of positrons, records detection signals only when a plurality of detectors detect the radioactive rays (gamma rays) simultaneously (that is, only when coincidences are counted), and performs a reconstruction process on the detection signals (numerous gamma ray detection signals) to create tomographic images of the subject. The SPECT apparatus detects a single radioactive ray (gamma ray), and performs a reconstruction process to create tomographic images of the subject.
To describe this by taking for example the nuclear medicine diagnostic apparatus (emission CT apparatus) such as the PET apparatus and SPECT apparatus, a reconstruction processing technique (ML reconstruction method) for an emission CT image based on maximum likelihood (ML: Maximum Likelihood) of Poisson distribution has been proposed in the field of emission CT apparatus (see Nonpatent Document 1, for example). In the image reconstruction technique used with the PET apparatus and SPECT apparatus today, although different from one apparatus maker to another, the mathematical framework (theory serving as a foundation) of almost all techniques is the ML reconstruction method described in Nonpatent Document 1. In this sense, in the field of emission CT apparatus, Nonpatent Document 1 is a very famous treatise about the ML reconstruction method. Almost all of today's image reconstruction methods can be said analogs of the technique described in Nonpatent Document 1.
A measurement data set (that is, measurement data) of a subject obtained by a radiation detecting apparatus includes statistical errors, and a distribution of statistical errors (error distribution) follows Poisson distribution. The ML reconstruction method described in Nonpatent Document 1 is a method for obtaining as a likely radioactivity distribution image (physical quantity distribution) a solution (image) which maximizes a likelihood function derived from Poisson characteristics of measurement data. When an extension is made to an error distribution (e.g. Gaussian distribution) other than Poisson distribution, as in the field of X-ray CT apparatus, the likelihood function is generally also called “data function”. The maximization of the likelihood function is performed using a repeated calculation algorithm (iterative method).
When the likelihood function of Poisson distribution is represented by L(x), the likelihood function L(x) of Poisson distribution is expressed by the following equation (1):
                    [                  Math          ⁢                                          ⁢          1                ]                                                                      L          ⁡                      (            x            )                          =                                            ∑                              i                =                1                            I                        ⁢                                          a                i                            ·              x                                -                                    ∑                              i                =                1                            I                        ⁢                                          y                i                            ⁢                              log                ⁡                                  (                                                                                    a                        i                                            ·                      x                                        +                                          r                      i                                                        )                                                                                        (        1        )            
Here, x is a reconstructed image vector (however, pixel values are non-negative), I is the number of measurement data points, ai is a sensitivity distribution function at an i-th measurement data point (an i-th row vector of system matrix A), yi is a prompt coincidence value (count value) at the i-th measurement data point, and ri is estimated values of count values of coincidences (random coincidences and scatter coincidences) other than the prompt coincidence value (count value) at the i-th measurement data point.